Thread: Problem on functions?

If α and β are multiplicative functions, prove that the function f(n) defined by f(n) = α(n)β(n)
is a multiplicative function.

suppose gcd(k,m) = 1.

then f(km) = α(km)β(km) = α(k)α(m)β(k)β(m) = α(k)β(k)α(m)β(m) = ?

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